All Algebra Basics in One Place!
To understand algebra deeply, you need to learn some basics first. This article will help you to start. It contains info that helps to go further in learning.
The high school encourages us to study many complex disciplines and one of them is Algebra. For many students, this is a challenging subject as it requires a deep understanding of math and being able to conduct operations like adding, subtracting, multiplying, dividing and their various combinations. In this article, you will learn how to cope with algebra challenges and ease the process of learning.
Main Things You Need to Know about Algebra
- All the math operations have to be used in a particular order. To remember it you can use the acronym PEMDAS.
- Know how to work with negative numbers. The main thing you need to understand that the bigger the number, the more distance from zero points.
- When you have a big task, divide it into smaller ones to organize the solving process. Start every new stage from the new line.
- Learn how to deal with variables that represented as letters (like x, y, z) and cannot perform number functions.
- When you have combines equations with letter and numbers, try to exclude any numbers during the available algebra operations.
As we already mentioned, one of the useful tricks can be the PEMDAS approach. This tool was designed to memorize the right math operation order. To cut the story short, we will not discuss in details why it is so, but only decode the acronym:
Shortly speaking, why this order is important in algebra, then you need to keep in mind that the wrong order will lead to the wrong results. For instance, when you have an issue like 8+7×4 and start with adding operation before multiplying, you will get 60, that will be definitely wrong. According to basic math rules you need to multiply the numbers first and then conduct the adding operations. Eventually, you will get 36 that will be the right result recognizable for everyone. To get the right answers all the time we have to follow this rule.
Basic Principles of Algebra
Let’s start with the main operations. The first thing will be arithmetic. Every student who learns algebra must know the principles of arithmetic. Since the elementary schools, we are being taught how to deal with adding, subtracting, multiplying and dividing. That is why most people do not have any difficulties with such tasks. Algebra, in general, is almost completely based on these operations. But the complexity of it lies in various formulas, equations and substitution of numbers with symbols. If you have any problems with understanding these aspects, you can learn them on your own using the available online resources and books on math. To obtain skills in algebra you need to learn the basics step by step.
If you think that working with numbers is not your passion, you have to realize that there is no need to be an expert in math to understand the main elements of algebra. Even if you study some humanitarian disciplines like journalism, law or languages, you still can learn some simplest equations first and train your counting skills. All the more complicated formulas and issues are required for students who plan to study accounting or statistics etc.
In some cases, students may be assigned to write academic papers on this subject and they may get benefits from special writing services to get high results and improve their skills. You also can use a calculator that may help in solving basic tasks and concentrate on more important ones. Also, some software like Excel can be helpful in solving algebra tasks with accuracy. In this case, you need to know how and when to use the available tools. These skills are required not only for students but for people who deal with similar issues.
But when it comes to exams, keep in mind that the only tools you are allowed to use there are your calculator and a pen. Any additional tools, devices, and helpful materials are forbidden there. To ease the process of taking such exams and save time you need to know perfectly how your calculator works and what problems it helps to solve.
How to Deal with Negative Numbers?
The biggest challenge for many pupils was the understanding that -/- gives + while -/+ remains the -. But this is the basic thing we had to memorize.
Negative numbers are used very often in algebra, accounting, statistics, economics, and other subjects that are related to math and you need to have particular knowledge. We can start with basic operations like adding, multiplying, subtracting and dividing to realize how everything works in order to move to the same processes with negatives.
- Keep in mind that negative number located on the same distance from zero as the positive equivalent, but the direction is the opposite. You can draw or imagine the line to make visual proof of what number is bigger.
- When you add one negative to another you get even more negative number. You see that the digit is higher, but it keeps its negative meaning with a minus sign. So it will be lower considering the number line.
- When you subtract the negatives, you can consider it as adding a positive number.
- When you divide or multiply negative numbers, you will always get a positive result.
- When you divide or multiply a negative number with a positive one, in this case, you will always get a negative result.
The Structure of Algebra Problems
Like when you work on a research paper or an essay, in solving algebra problems you should follow the particular structure as well. Yes, you probably will need to provide a short answer, but the whole process of solving should be displayed on paper in a particular order to follow your thoughts.
This is really important when you have to deal with long problems. They may have various approaches for solving, and each of them may require a lot of time. If you do not want to miss anything or make a mistake, you need to start every new step with a new line and number each line. If you have a problem with the two-sided equation, then it is better to put every part of the solving process under each other. This will let you control the process and spot any possible mistakes quickly.
For instance, if you have to solve the equation 12/6 – 2 + 5 x4, you should organize your work in the following way:
12/6 – 2 + 5 x4
12/6 – 2 + 20
2 – 2 + 12
0 + 12
This approach applies to any algebra problem. When you organize it in the step-by-step order, you will make your learning more effective.
How to Work with Variables and Their Definition
If you have to pass the SAT, then you need to know algebra well. So you need to understand at least the main principles first. Learn more about SAT test scores and find any other useful info on this aspect. Reaching satisfactory results will help you with entering college.
One of the primary conditions is knowledge of what variables are and how to work with them. In SAT you will definitely have tasks with these elements. Also, sometimes we add letters and symbols to the numbers. As a rule, they serve as a substitution to the unknown numbers when you need an extra figure to fit the formula, for instance.
That is why they are called variables. We do not know their value, and in some cases, it is not easy to discover it. However, you sometimes even do not have to see the value to solve the task. All you need is to use the right formulas and interpret the right.
Here are the examples of variables used in algebra:
- Latin letters like a, b, c, x, y…;
- Greek letters like theta or beta;
- the symbol pi, or π, also is considered as a variable.
In any case, you should consider these symbols as unknown numbers. In most tasks, you need to find the value of the unknown numbers by using the basic formulas. Here is the example of such tasks:
6x+6=18, where we have X as a variable. This means that we do not know its value but we can define it using the information from other numbers. We need to make both sides equal to 18. We subtract the 6 from 18 and have 12. As we know, 6×2=12, then we have found out that X means 2.
Another approach to understanding the variables is the substituting them with question marks. For example, you need to solve the equation 2+5+x=15, so imagine it as 2+5+?=15. It is obvious that the answer here is 8.
But how to act if you have more than one variable in your task? This can be solved simply in algebra as well. Consider them as a regular number in this case. Any arithmetical operations can be done with variables of the same meaning.
When x+x=3x, then x+y will have another meaning (for instance, 3xy).
Let’s discover how this works with this equation: 1x+3x=8. You can add parts 1x and 3x as they have the same variable and you will get 4x. Since we have 4x=8, then we can easily assume that x=2. But this approach is applicable to the same variable only.
“Cancelling” Principle: How it Works
You can get the variable in another way. When we have an equation, we may have numbers and variables from both sides. For example, you may have a task like x+5=8×3. You need to separate the variables from the numbers. So we need to exclude the number “5” from the right side and put it on the left. But you have to do so by changing its positive meaning to the negative one. So you will get an equation like this: x=8×3-5. Now you need simply to solve the basic math task and you will get: x=24-5=19. A piece of cake.
Let’s discuss how we can to cancel the addition. When we have the unknown number on one side, this means we can replace the known numbers on another one. We have to conduct the opposite operation. As we know, adding and subtracting are the opposite operations. That is why in our example we have subtracted the 5 to compensate its missing on the first side. This is one of the basics of algebra that you need to know for sure.
You can also use this principle when you deal with multiplication and division. As you can see, starting understanding algebra can be not so hard.
Train Your Skills More
If you feel that you need more training to memorize algebra basics, you can use the visual elements to get the info better. You can use images in order to illustrate any algebra issue like formulas, equations, etc. During lessons teachers sometimes use any available physical objects to enhance the understanding of the concepts.
How to deal with “common sense check”? This is one more opportunity to get deeper algebra insight. Anytime you present a written problem with the algebraic elements. You can check the formula by using the simple numbers. You can choose whether the equation is meaningful by replacing x with 0 or 1.
Moreover, you do not always have to get around or straightforward number after solving the math problem. The answer may contain irrational numbers, decimals, fractions, and others. This is the reason you should bring the calculator. You will be informed of what form will be suitable for each problem.
If you are confident in your algebra skills, check how you deal with factoring. This is one of the most complicated aspects of math. This approach is used to make the ling equations shorter and simpler. This section is considered as semi-advanced algebra.
You can practice by applying algebra approaches to real-life situations. To get the algebra better, you should not only memorize the formulas but to use them and practice. This is the only way you will keep in mind at least basics.
If you deal with finances, you can train your skills as well. Part-time or season job can also be useful in practicing your skills. You can also use your knowledge for obtaining related disciplines like accounting, economics, etc. By the way, math, and algebra, in particular, is also required for understanding computer sciences. This discipline is vital for engineering and constructing too.
If you still consider that you cannot solve the math or algebra problem correctly, you can ask for professional assistance and order the writing help from experts who will help you to shape and correct your solutions.